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Mathematical rules provide tape measure for estimating size of ancient marine reptiles from partial fossils

Mathematical rules provide a tape measure for estimating size of ancient marine reptiles from partial fossils
3D model of the ichthyosaur Eurhinosaurus longirostris, from the Muséum National d’Histoire Naturelle (Paris, France), showing the different measurements used in the study. Credit: Université de Liège / Evolution & Diversity Dynamics Lab

How can we guess the size of an extinct animal when all that remains are a few scattered bones? A study conducted by researchers at ULiège now provides an answer to this question. Using mathematical methods applied to hundreds of measurements, they have established rules that can now be used to calculate the total length of marine reptiles that lived more than 100 million years ago.

The work is in the journal Biology Letters.

"For decades, have been struggling with this major difficulty," explains Prof. Valentin Fischer, paleontologist and director of the Evolution & Diversity Dynamics Lab. "Most fossil skeletons of large marine reptiles such as ichthyosaurs, mosasaurs, and marine crocodiliformes are incomplete. Under these conditions, it is difficult to accurately estimate the size of these animals that dominated the seas of the Mesozoic era."

The research team set about compiling and analyzing hundreds of of specimens known from complete skeletons. They then tested 23 measurements—trunk length, vertebral dimensions, fin proportions, etc.—to identify which were the best indicators of total size.

They were then able to deduce that certain elements of the skeleton, such as trunk length or vertebral dimensions, are in fact excellent predictors of an animal's total length, but that each group has equations that are distinct from the others. This long-term project has made it possible, for the first time, to propose equations that can be made available to the to estimate the size of marine reptiles from fossil fragments.

This breakthrough opens up new possibilities. "The size of an animal is a key factor in its ecology," explains Fischer. "Thanks to these equations, we will be able to build vast databases on the evolution of marine predator sizes throughout past ecological crises."

In other words, we will be able to understand how these marine monsters grew, shrank or disappeared as their environment changed.

More information: Valentin Fischer et al, Predicting body length and assessing the shape of tail-propelled Mesozoic marine reptiles, Biology Letters (2025).

Journal information: Biology Letters

Provided by University de Liege

Citation: Mathematical rules provide tape measure for estimating size of ancient marine reptiles from partial fossils (2025, September 24) retrieved 11 November 2025 from /news/2025-09-mathematical-tape-size-ancient-marine.html
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